Download 7.7 Squares Worksheet

Key
Advanced Geometry
Worksheet 7.7: Squares
Name:_______________________
Answer each question
1. A square has all the properties of a rhombus and rectangle. List the properties a square gets
from both special parallelograms
From Rhombus
From Rectangle
angles
All sides are congruent
All
are
I
-
perpendicular to
are
Diagonals
each other
which
Diagonals bisect the angles
they
are
drawn to
-
Diagonals
be
a
right
.
need
and all angles
congruent
angles
but
,
congruent
are
.
2. Explain why this statement is false. “Every rhombus is a square.”
has to have all side
Because a
square
right
angler
-
a
angles
square
rhombus only needs to have
all
to
sides congruent
.
all angles need to
and
congruent
angles
her to have all
3. Explain why this statement is false. “Every rectangle is a square.”
has to have all side
Because a
be
a
right
,
but
a
rectangle only
right
.
4. ACGH is a square. Find the measure of each missing angle
6
M< KGO
1
2
3
m<
5
4
Mc
'
2=90
3=90
m<
4=45
Mc
5=45
m<
'
a
6=90
For 5 – 7: Use the figure to the right
5. Using the distance formula, show the quadrilateral is a rhombus.
dan
Etch
t.cm#=4.47
d.
=
=
den
dBc=
FEET
tetchy
447
It's a rhombus because
all sides are I
4.47
=
.
=
4.47
6. Using the slope formula, show the shape is a rectangle. (Perpendicular lines have opposite sign,
reciprocal slopes)
'¥¥±÷IIts
Terse
m←It¥=¥
's
-
2
other the
,
lines
are
perpendicular
sina.tk?FoaEeoteauMBc=#3h=Is.=
7. What is the most specific way to classify quadrilateral ADCB?
all
creating right angles for
corner
angles
.
Square
.
the
Determine if the state is ALWAYS, SOMETIMES, or NEVER true.
8.
A parallelogram is a square
9.
A square is a rhombus
10.
Sometimes
Always
A rectangle is a parallelogram
Always
11. A rhombus is a rectangle
Sometimes
12. A rhombus is a square
sometimes
13. A square is a rectangle
Always
Solve for x. The quadrilateral is a square.
14. The perimeter is 52 ft.
15.
13
3×-2=13
13
72+72×2
7
31=15
3x – 2
,
7 cm
x cm
X€
}
9S=×2
9.9€
7
The shapes below is a parallelogram with all sides congruent. Solve for x. Then determine if the
most specific name for the parallelogram is a square or a rhombus? Explain your reasoning. The
shapes are NOT drawn to scale.
(3x – 27)o
16.
%
90
a
(2x +12)o
go
.
3×-27+2×+12=180
Square because
allangwar
right angles
(4x – 8)o
17.
72
logo
'
'
72
(2x +14)o
Rhombus
tnhffingshtoanageo
logo
.
4×-8+2×+14=180
6×+6=180
5×-15=180
GX
511=195
×=39
-
174
11=29
18. Classify the polygons as specifically as possible (quadrilateral, parallelogram, rhombus,
rectangle, square).The figures are NOT drawn to scale.
o
o
o
90
Rhombus
parallelogram
o
90
square
o
o
90
90
90
90
o
90
o
90
Rectangle
,
square